Thatched Hut Hearth Smoke

What is modelled

A fire heats a small share of its power into the air of the hut. The warm air is lighter than the outside air, so it rises out through the thatch and fresh air is drawn in at the door. Wind adds its own flow. The carbon monoxide made by the fire is mixed through the whole hut at once and carried away by that flow, so its level rises towards a steady value set by the emission divided by the ventilation flow.

Equations

• Stack flow Qs = Cd Ae √(2 g H ΔT / T), wind flow Qw = Cv Ae u, total Q = √(Qs2 + Qw2).
• Heat balance φ P = (ρ cp Q + U A) ΔT.
• Concentration V dC/dt = G − Q C, steady C = G / Q, time constant τ = V / Q.

Checks run in the page

• RK4 integration against the closed form at two time constants.
• Emitted mass equals stored plus removed mass.
• Bisection against a damped fixed-point iteration for the stack balance.
• Time to a guideline by stepping against the logarithm formula.

Honest simplifications

The hut air is perfectly mixed, the fire is steady for four hours, the heat share, discharge coefficients and the thatch leakage are typical round values and outdoor carbon monoxide is zero. Real huts have strong gradients near the fire and variable leakage. The guideline lines are the 1 hour and 8 hour values quoted by the World Health Organization for indoor air.

• Press Open fire, door shut and watch the level pass the one-hour line.
• Press Improved stove and compare the steady value.
• Press Windy day to see the wind term take over from the stack effect.